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For $s > 0$, $s \neq 1$, bilinear Fourier multipliers of the form $e^{i (|\xi|^s + |\eta|^s+ |\xi + \eta|^s)} \sigma (\xi, \eta)$ are considered, where $\sigma(\xi, \eta)$ belongs to the H\"ormander class $S^{m}_{1, 0}(\mathbb{R}^{2n})$. A criterion for $m$ to ensure the $L^{\infty}\times L^{\infty} \to L^\infty$, $L^{1} \times L^{\infty} \to L^{1}$, and $L^{\infty} \times L^{1} \to L^{1}$ boundedness of the corresponding bilinear operators is given., Comment: 17 pages

Off-road environments present significant challenges for autonomous ground vehicles due to the absence of structured roads and the presence of complex obstacles, such as uneven terrain, vegetation, and occlusions. Traditional perception algorithms, designed primarily for structured environments, often fail under these conditions, leading to inaccurate traversability estimations. In this paper, ORDformer, a novel multimodal method that combines LiDAR point clouds with monocular images, is proposed to generate dense traversable occupancy predictions from a forward-facing perspective. By integrating multimodal data, environmental feature extraction is enhanced, which is crucial for accurate occupancy estimation in complex terrains. Furthermore, RELLIS-OCC, a dataset with 3D traversable occupancy annotations, is introduced, incorporating geometric features such as step height, slope, and unevenness. Through a comprehensive analysis of vehicle obstacle-crossing conditions and the incorporation of vehicle body structure constraints, four traversability cost labels are generated: lethal, medium-cost, low-cost, and free. Experimental results demonstrate that ORDformer outperforms existing approaches in 3D traversable area recognition, particularly in off-road environments with irregular geometries and partial occlusions. Specifically, ORDformer achieves over a 20\% improvement in scene completion IoU compared to other models. The proposed framework is scalable and adaptable to various vehicle platforms, allowing for adjustments to occupancy grid parameters and the integration of advanced dynamic models for traversability cost estimation., Comment: 12 pages,14 figures

In this paper, we propose two regularized proximal quasi-Newton methods with symmetric rank-1 update of the metric (SR1 quasi-Newton) to solve non-smooth convex additive composite problems. Both algorithms avoid using line search or other trust region strategies. For each of them, we prove a super-linear convergence rate that is independent of the initialization of the algorithm. The cubic regularized method achieves a rate of order $\left(\frac{C}{N^{1/2}}\right)^{N/2}$, where $N$ is the number of iterations and $C$ is some constant, and the other gradient regularized method shows a rate of the order $\left(\frac{C}{N^{1/4}}\right)^{N/2}$. To the best of our knowledge, these are the first global non-asymptotic super-linear convergence rates for regularized quasi-Newton methods and regularized proximal quasi-Newton methods. The theoretical properties are also demonstrated in two applications from machine learning.

Modern QA systems entail retrieval-augmented generation (RAG) for accurate and trustworthy responses. However, the inherent gap between user queries and relevant documents hinders precise matching. Motivated by our conical distribution hypothesis, which posits that potential queries and documents form a cone-like structure in the embedding space, we introduce QAEncoder, a training-free approach to bridge this gap. Specifically, QAEncoder estimates the expectation of potential queries in the embedding space as a robust surrogate for the document embedding, and attaches document fingerprints to effectively distinguish these embeddings. Extensive experiments on fourteen embedding models across six languages and eight datasets validate QAEncoder's alignment capability, which offers a plug-and-play solution that seamlessly integrates with existing RAG architectures and training-based methods.

Distributionally robust optimal control (DROC) is gaining interest. This study presents a reformulation method for discrete DROC (DDROC) problems to design optimal control policies under a worst-case distributional uncertainty. The reformulation of DDROC problems impacts both the utility of tractable improvements in continuous DROC problems and the inherent discretization modeling of DROC problems. DROC is believed to have tractability issues; namely, infinite inequalities emerge over the distribution space. Therefore, investigating tractable reformulation methods for these DROC problems is crucial. One such method utilizes the strong dualities of the worst-case expectations. However, previous studies demonstrated that certain non-trivial inequalities remain after the reformulation. To enhance the tractability of DDROC, the proposed method reformulates DDROC problems into one-layer smooth convex programming with only a few trivial inequalities. The proposed method is applied to a DDROC version of a patrol-agent design problem., Comment: 7 pages, 1 figure, This work has been submitted to the IEEE for possible publication

Non-line-of-sight (NLOS) imaging, recovering the hidden volume from indirect reflections, has attracted increasing attention due to its potential applications. Despite promising results, existing NLOS reconstruction approaches are constrained by the reliance on empirical physical priors, e.g., single fixed path compensation. Moreover, these approaches still possess limited generalization ability, particularly when dealing with scenes at a low signal-to-noise ratio (SNR). To overcome the above problems, we introduce a novel learning-based solution, comprising two key designs: Learnable Path Compensation (LPC) and Adaptive Phasor Field (APF). The LPC applies tailored path compensation coefficients to adapt to different objects in the scene, effectively reducing light wave attenuation, especially in distant regions. Meanwhile, the APF learns the precise Gaussian window of the illumination function for the phasor field, dynamically selecting the relevant spectrum band of the transient measurement. Experimental validations demonstrate that our proposed approach, only trained on synthetic data, exhibits the capability to seamlessly generalize across various real-world datasets captured by different imaging systems and characterized by low SNRs.

Battery management is a critical component of ubiquitous battery-powered energy systems, in which battery state-of-charge (SOC) and state-of-health (SOH) estimations are of crucial importance. Conventional SOC and SOH estimation methods, especially model-based methods, often lack accurate modeling of the open circuit voltage (OCV), have relatively high computational complexity, and lack theoretical analysis. This study introduces a simple SOC and SOH estimation method that overcomes all these weaknesses. The key idea of the proposed method is to momentarily set the cell's current to zero for a few minutes during the charging, perform SOC and SOH estimation based on the measured data, and continue tracking the cell's SOC afterward. The method is based on rigorous theoretical analysis, requires no hyperparameter fine-tuning, and is hundreds of times faster than conventional model-based methods. The method is validated on six batteries charged at different C rates and temperatures, realizing fast and accurate estimations under various conditions, with a SOH root mean square error (RMSE) of around 3% and a SOC RMSE of around 1.5%., Comment: Minor changes to texts and figures

The Kalman filter (KF) is a state estimation algorithm that optimally combines system knowledge and measurements to minimize the mean squared error of the estimated states. While KF was initially designed for linear systems, numerous extensions of it, such as extended Kalman filter (EKF), unscented Kalman filter (UKF), cubature Kalman filter (CKF), etc., have been proposed for nonlinear systems. Although different types of nonlinear KFs have different pros and cons, they all use the same framework of linear KF. Yet, according to what we found in this paper, the framework tends to give overconfident and less accurate state estimations when the measurement functions are nonlinear. Therefore, in this study, we designed a new framework that can be combined with any existing type of nonlinear KFs and showed theoretically and empirically that the new framework estimates the states and covariance more accurately than the old one. The new framework was tested on four different nonlinear KFs and five different tasks, showcasing its ability to reduce estimation errors by several orders of magnitude in low-measurement-noise conditions., Comment: Some final changes before submission

In this paper, we address the problem of plausible object placement for the challenging task of realistic image composition. We propose DiffPop, the first framework that utilizes plausibility-guided denoising diffusion probabilistic model to learn the scale and spatial relations among multiple objects and the corresponding scene image. First, we train an unguided diffusion model to directly learn the object placement parameters in a self-supervised manner. Then, we develop a human-in-the-loop pipeline which exploits human labeling on the diffusion-generated composite images to provide the weak supervision for training a structural plausibility classifier. The classifier is further used to guide the diffusion sampling process towards generating the plausible object placement. Experimental results verify the superiority of our method for producing plausible and diverse composite images on the new Cityscapes-OP dataset and the public OPA dataset, as well as demonstrate its potential in applications such as data augmentation and multi-object placement tasks. Our dataset and code will be released.

In this paper, we investigate the length-extension of state-space models (SSMs) in language modeling. Length extension involves training models on short sequences and testing them on longer ones. We show that state-space models trained with zero hidden states initialization have difficulty doing length extension. We explain this difficulty by pointing out the length extension is equivalent to polynomial extrapolation. Based on the theory, we propose a simple yet effective method - changing the hidden states initialization scheme - to improve the length extension. Moreover, our method shows that using long training sequence length is beneficial but not necessary to length extension. Changing the hidden state initialization enables the efficient training of long-memory model with a smaller training context length., Comment: 23 pages

Quasi-Newton methods refer to a class of algorithms at the interface between first and second order methods. They aim to progress as substantially as second order methods per iteration, while maintaining the computational complexity of first order methods. The approximation of second order information by first order derivatives can be expressed as adopting a variable metric, which for (limited memory) quasi-Newton methods is of type ``identity $\pm$ low rank''. This paper continues the effort to make these powerful methods available for non-smooth systems occurring, for example, in large scale Machine Learning applications by exploiting this special structure. We develop a line search variant of a recently introduced quasi-Newton primal-dual algorithm, which adds significant flexibility, admits larger steps per iteration, and circumvents the complicated precalculation of a certain operator norm. We prove convergence, including convergence rates, for our proposed method and outperform related algorithms in a large scale image deblurring application.

In this paper, we study for the first time the Diverse Longest Common Subsequences (LCSs) problem under Hamming distance. Given a set of a constant number of input strings, the problem asks to decide if there exists some subset $\mathcal X$ of $K$ longest common subsequences whose diversity is no less than a specified threshold $\Delta$, where we consider two types of diversities of a set $\mathcal X$ of strings of equal length: the Sum diversity and the Min diversity defined as the sum and the minimum of the pairwise Hamming distance between any two strings in $\mathcal X$, respectively. We analyze the computational complexity of the respective problems with Sum- and Min-diversity measures, called the Max-Sum and Max-Min Diverse LCSs, respectively, considering both approximation algorithms and parameterized complexity. Our results are summarized as follows. When $K$ is bounded, both problems are polynomial time solvable. In contrast, when $K$ is unbounded, both problems become NP-hard, while Max-Sum Diverse LCSs problem admits a PTAS. Furthermore, we analyze the parameterized complexity of both problems with combinations of parameters $K$ and $r$, where $r$ is the length of the candidate strings to be selected. Importantly, all positive results above are proven in a more general setting, where an input is an edge-labeled directed acyclic graph (DAG) that succinctly represents a set of strings of the same length. Negative results are proven in the setting where an input is explicitly given as a set of strings. The latter results are equipped with an encoding such a set as the longest common subsequences of a specific input string set., Comment: Proceedings of 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024), Leibniz International Proceedings in Informatics, Vol.296, pp.21:0-21:17, June 2024

Multi-object transport using multi-robot systems has the potential for diverse practical applications such as delivery services owing to its efficient individual and scalable cooperative transport. However, allocating transportation tasks of objects with unknown weights remains challenging. Moreover, the presence of infeasible tasks (untransportable objects) can lead to robot stoppage (deadlock). This paper proposes a framework for dynamic task allocation that involves storing task experiences for each task in a scalable manner with respect to the number of robots. First, these experiences are broadcasted from the cloud server to the entire robot system. Subsequently, each robot learns the exclusion levels for each task based on those task experiences, enabling it to exclude infeasible tasks and reset its task priorities. Finally, individual transportation, cooperative transportation, and the temporary exclusion of tasks considered infeasible are achieved. The scalability and versatility of the proposed method were confirmed through numerical experiments with an increased number of robots and objects, including unlearned weight objects. The effectiveness of the temporary deadlock avoidance was also confirmed by introducing additional robots within an episode. The proposed method enables the implementation of task allocation strategies that are feasible for different numbers of robots and various transport tasks without prior consideration of feasibility., Comment: 8 pages, 10 figures

For bilinear Fourier multipliers that contain some oscillatory factors, boundedness of the operators between Lebesgue spaces is given including endpoint cases. Sharpness of the result is also considered., Comment: 27 pages, 1 figure

Predictable forward performance processes (PFPPs) are stochastic optimal control frameworks for an agent who controls a randomly evolving system but can only prescribe the system dynamics for a short period ahead. This is a common scenario in which a controlling agent frequently re-calibrates her model. We introduce a new class of PFPPs based on rank-dependent utility, generalizing existing models that are based on expected utility theory (EUT). We establish existence of rank-dependent PFPPs under a conditionally complete market and exogenous probability distortion functions which are updated periodically. We show that their construction reduces to solving an integral equation that generalizes the integral equation obtained under EUT in previous studies. We then propose a new approach for solving the integral equation via theory of Volterra equations. We illustrate our result in the special case of conditionally complete Black-Scholes model., Comment: 43 pages, 3 figures

N-terminal coding sequence (NCS) influences gene expression by impacting the translation initiation rate. The NCS optimization problem is to find an NCS that maximizes gene expression. The problem is important in genetic engineering. However, current methods for NCS optimization such as rational design and statistics-guided approaches are labor-intensive yield only relatively small improvements. This paper introduces a deep learning/synthetic biology co-designed few-shot training workflow for NCS optimization. Our method utilizes k-nearest encoding followed by word2vec to encode the NCS, then performs feature extraction using attention mechanisms, before constructing a time-series network for predicting gene expression intensity, and finally a direct search algorithm identifies the optimal NCS with limited training data. We took green fluorescent protein (GFP) expressed by Bacillus subtilis as a reporting protein of NCSs, and employed the fluorescence enhancement factor as the metric of NCS optimization. Within just six iterative experiments, our model generated an NCS (MLD62) that increased average GFP expression by 5.41-fold, outperforming the state-of-the-art NCS designs. Extending our findings beyond GFP, we showed that our engineered NCS (MLD62) can effectively boost the production of N-acetylneuraminic acid by enhancing the expression of the crucial rate-limiting GNA1 gene, demonstrating its practical utility. We have open-sourced our NCS expression database and experimental procedures for public use.

In this paper, we present a novel ciphertext-policy attribute based encryption (CP-ABE) scheme that offers a flexible access structure. Our proposed scheme incorporates an access tree as its access control policy, enabling fine-grained access control over encrypted data. The security of our scheme is provable under the hardness assumption of the decisional Ring-Learning with Errors (R-LWE) problem, ensuring robust protection against unauthorized access. CP-ABE is a cryptographic technique that allows data owners to encrypt their data with access policies defined in terms of attributes. Only users possessing the required attributes can decrypt and access the encrypted data. Our scheme extends the capabilities of CP-ABE by introducing a flexible access structure based on an access tree. This structure enables more complex and customizable access policies, accommodating a wider range of real-world scenarios. To ensure the security of our scheme, we rely on the decisional R-LWE problem, a well-established hardness assumption in cryptography. By proving the security of our scheme under this assumption, we provide a strong guarantee of protection against potential attacks. Furthermore, our proposed scheme operates in the standard model, which means it does not rely on any additional assumptions or idealized cryptographic primitives. This enhances the practicality and applicability of our scheme, making it suitable for real-world deployment. We evaluate the performance and efficiency of our scheme through extensive simulations and comparisons with existing CP-ABE schemes. The results demonstrate the effectiveness and scalability of our proposed approach, highlighting its potential for secure and flexible data access control in various domains., Comment: 10 pages

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets, language models and image classifications., Comment: 28 pages, 7 figures, ICML 2024